The statistical distribution of a random variable describes the probabilities of its possible outcomes
and hence their relative frequencies in repeated trials. For a real-valued random variable 
, the distribution function
(or cumulative distribution function, abbreviated CDF) is 
. In the discrete
case, the probability mass function gives
.
When a probability density function 
exists, probabilities of intervals are given by integrals,
.
Formally, a statistical distribution is a probability measure. Let 
be a random variable from
a probability space 
into a measurable space 
.
Its distribution is the measure 
on 
defined by
 |
where 
.
A statistical distribution on 
that is a Radon measure
can also be viewed as a generalized function.
